
(/VERSIONCHECK 2) 

(DEFPARAMETER |FiniteRankNonAssociativeAlgebra;CAT| 'NIL) 

(DEFPARAMETER |FiniteRankNonAssociativeAlgebra;AL| 'NIL) 

(DEFUN |FiniteRankNonAssociativeAlgebra| (#1=#:G1818)
  (LET (#2=#:G1819)
    (COND
     ((SETQ #2#
              (|assoc| #3=(|devaluate| #1#)
                       |FiniteRankNonAssociativeAlgebra;AL|))
      (CDR #2#))
     (T
      (SETQ |FiniteRankNonAssociativeAlgebra;AL|
              (|cons5|
               (CONS #3# (SETQ #2# (|FiniteRankNonAssociativeAlgebra;| #1#)))
               |FiniteRankNonAssociativeAlgebra;AL|))
      #2#)))) 

(DEFUN |FiniteRankNonAssociativeAlgebra;| (|t#1|)
  (PROG (#1=#:G1817)
    (RETURN
     (PROG1
         (LETT #1#
               (|sublisV| (PAIR '(|t#1|) (LIST (|devaluate| |t#1|)))
                          (COND (|FiniteRankNonAssociativeAlgebra;CAT|)
                                ('T
                                 (LETT |FiniteRankNonAssociativeAlgebra;CAT|
                                       (|Join| (|NonAssociativeAlgebra| '|t#1|)
                                               (|mkCategory|
                                                '(((|someBasis| ((|Vector| $)))
                                                   T)
                                                  ((|rank|
                                                    ((|PositiveInteger|)))
                                                   T)
                                                  ((|conditionsForIdempotents|
                                                    ((|List|
                                                      (|Polynomial| |t#1|))
                                                     (|Vector| $)))
                                                   T)
                                                  ((|structuralConstants|
                                                    ((|Vector|
                                                      (|Matrix| |t#1|))
                                                     (|Vector| $)))
                                                   T)
                                                  ((|leftRegularRepresentation|
                                                    ((|Matrix| |t#1|) $
                                                     (|Vector| $)))
                                                   T)
                                                  ((|rightRegularRepresentation|
                                                    ((|Matrix| |t#1|) $
                                                     (|Vector| $)))
                                                   T)
                                                  ((|leftTrace| (|t#1| $)) T)
                                                  ((|rightTrace| (|t#1| $)) T)
                                                  ((|leftNorm| (|t#1| $)) T)
                                                  ((|rightNorm| (|t#1| $)) T)
                                                  ((|coordinates|
                                                    ((|Vector| |t#1|) $
                                                     (|Vector| $)))
                                                   T)
                                                  ((|coordinates|
                                                    ((|Matrix| |t#1|)
                                                     (|Vector| $)
                                                     (|Vector| $)))
                                                   T)
                                                  ((|represents|
                                                    ($ (|Vector| |t#1|)
                                                     (|Vector| $)))
                                                   T)
                                                  ((|leftDiscriminant|
                                                    (|t#1| (|Vector| $)))
                                                   T)
                                                  ((|rightDiscriminant|
                                                    (|t#1| (|Vector| $)))
                                                   T)
                                                  ((|leftTraceMatrix|
                                                    ((|Matrix| |t#1|)
                                                     (|Vector| $)))
                                                   T)
                                                  ((|rightTraceMatrix|
                                                    ((|Matrix| |t#1|)
                                                     (|Vector| $)))
                                                   T)
                                                  ((|leftCharacteristicPolynomial|
                                                    ((|SparseUnivariatePolynomial|
                                                      |t#1|)
                                                     $))
                                                   T)
                                                  ((|rightCharacteristicPolynomial|
                                                    ((|SparseUnivariatePolynomial|
                                                      |t#1|)
                                                     $))
                                                   T)
                                                  ((|commutative?|
                                                    ((|Boolean|)))
                                                   T)
                                                  ((|antiCommutative?|
                                                    ((|Boolean|)))
                                                   T)
                                                  ((|associative?|
                                                    ((|Boolean|)))
                                                   T)
                                                  ((|antiAssociative?|
                                                    ((|Boolean|)))
                                                   T)
                                                  ((|leftAlternative?|
                                                    ((|Boolean|)))
                                                   T)
                                                  ((|rightAlternative?|
                                                    ((|Boolean|)))
                                                   T)
                                                  ((|flexible?| ((|Boolean|)))
                                                   T)
                                                  ((|alternative?|
                                                    ((|Boolean|)))
                                                   T)
                                                  ((|powerAssociative?|
                                                    ((|Boolean|)))
                                                   T)
                                                  ((|jacobiIdentity?|
                                                    ((|Boolean|)))
                                                   T)
                                                  ((|lieAdmissible?|
                                                    ((|Boolean|)))
                                                   T)
                                                  ((|jordanAdmissible?|
                                                    ((|Boolean|)))
                                                   T)
                                                  ((|noncommutativeJordanAlgebra?|
                                                    ((|Boolean|)))
                                                   T)
                                                  ((|jordanAlgebra?|
                                                    ((|Boolean|)))
                                                   T)
                                                  ((|lieAlgebra?|
                                                    ((|Boolean|)))
                                                   T)
                                                  ((|recip|
                                                    ((|Union| $ "failed") $))
                                                   (|has| |t#1|
                                                          (|IntegralDomain|)))
                                                  ((|leftRecip|
                                                    ((|Union| $ "failed") $))
                                                   (|has| |t#1|
                                                          (|IntegralDomain|)))
                                                  ((|rightRecip|
                                                    ((|Union| $ "failed") $))
                                                   (|has| |t#1|
                                                          (|IntegralDomain|)))
                                                  ((|associatorDependence|
                                                    ((|List|
                                                      (|Vector| |t#1|))))
                                                   (|has| |t#1|
                                                          (|IntegralDomain|)))
                                                  ((|leftMinimalPolynomial|
                                                    ((|SparseUnivariatePolynomial|
                                                      |t#1|)
                                                     $))
                                                   (|has| |t#1|
                                                          (|IntegralDomain|)))
                                                  ((|rightMinimalPolynomial|
                                                    ((|SparseUnivariatePolynomial|
                                                      |t#1|)
                                                     $))
                                                   (|has| |t#1|
                                                          (|IntegralDomain|)))
                                                  ((|leftUnits|
                                                    ((|Union|
                                                      (|Record|
                                                       (|:| |particular| $)
                                                       (|:| |basis|
                                                            (|List| $)))
                                                      "failed")))
                                                   (|has| |t#1|
                                                          (|IntegralDomain|)))
                                                  ((|rightUnits|
                                                    ((|Union|
                                                      (|Record|
                                                       (|:| |particular| $)
                                                       (|:| |basis|
                                                            (|List| $)))
                                                      "failed")))
                                                   (|has| |t#1|
                                                          (|IntegralDomain|)))
                                                  ((|leftUnit|
                                                    ((|Union| $ "failed")))
                                                   (|has| |t#1|
                                                          (|IntegralDomain|)))
                                                  ((|rightUnit|
                                                    ((|Union| $ "failed")))
                                                   (|has| |t#1|
                                                          (|IntegralDomain|)))
                                                  ((|unit|
                                                    ((|Union| $ "failed")))
                                                   (|has| |t#1|
                                                          (|IntegralDomain|))))
                                                '(((|unitsKnown|)
                                                   (|has| |t#1|
                                                          (|IntegralDomain|))))
                                                '((|SparseUnivariatePolynomial|
                                                   |t#1|)
                                                  (|List| (|Vector| |t#1|))
                                                  (|Boolean|) (|Matrix| |t#1|)
                                                  (|Vector| $) (|Vector| |t#1|)
                                                  (|Vector| (|Matrix| |t#1|))
                                                  (|List| (|Polynomial| |t#1|))
                                                  (|PositiveInteger|))
                                                NIL))
                                       . #2=(|FiniteRankNonAssociativeAlgebra|)))))
               . #2#)
       (SETELT #1# 0
               (LIST '|FiniteRankNonAssociativeAlgebra|
                     (|devaluate| |t#1|))))))) 
